truncAIPW: Doubly Robust Estimation under Covariate-induced Dependent Left Truncation and No Censoring

Description

Doubly robust estimation for the mean of an arbitrarily transformed survival time under covariate-induced dependent left truncation and no right censoring.

Usage

truncAIPW(dat, nu, Fuz.mx, Gvz.mx, T.name, Q.name, trim = 1e-07)

Value

truncAIPW() returns a list of estimators (`dr', `IPW.Q', `Reg.T1', `Reg.T2'), and the model-based standard errors for the `dr' and `IPW.Q' estimators.

dr: doubly robust estimator `dr'.
IPW.Q: inverse probability of truncation weighted estimator `IPW.Q'.
Reg.T1: regression based estimator `Reg.T1'.
Reg.T2: regression based estimator `Reg.T2'.
SE_dr: standard error of the `dr' estimator based on the efficient influence function.
SE_IPW.Q: standard error of the `IPW.Q' estimator computed from the robust sandwich variance estimator assuming the truncation weights are known.

Arguments

dat: data frame that contains the data for constructing the estimating equation.
nu: transformation that defines the parameter of interest.
Fuz.mx: matrix for the estimated conditional CDF of the event time given covariates. Each row corresponds to a subject, and each column corresponds to a time point. The column names of the matrix are the time points. See F_est for an example of computing this conditional CDF matrix.
Gvz.mx: matrix for the estimated conditional CDF of the truncation time given covariates. Each row corresponds to a subject, and each column corresponds to a time point. The column names of the matrix are the time points. See G_est for an example of computing this conditional CDF matrix.
T.name: name of the event time variable.
Q.name: name of the left truncation time variable.
trim: constant that is used to bound from below for the denominators involved in the computation.

References

Wang, Y., Ying, A., Xu, R. (2022) "Doubly robust estimation under covariate-induced dependent left truncation" <arXiv:2208.06836>.

Examples

Run this code

data("simu")
nu <- function(t){ return(as.numeric(t>3)) }
u = c(min(simu$time)-1e-10, sort(simu$time), max(simu$time)+1e-10)
v = c(min(simu$Q)-1e-10, sort(simu$Q), max(simu$Q)+1e-10)
Fuz.mx = F_est(simu, simu, u, "Cox", "time", "Q", "delta", c("Z1","Z2"))
Gvz.mx = G_est(simu, simu, v, "Cox", "time", "Q", "delta", c("Z1","Z2"))

est = truncAIPW(simu, nu, Fuz.mx, Gvz.mx, "time", "Q", trim = 1e-7)
est